Question

By using slopes, show that the following points are collinear
$P(5,0)$, $Q(10,-3)$, $R(-5,6)$

Answer 1

$P(5,0),Q(10,-3),R(-5,6)$

$\therefore$ Slope of $PQ=\frac{-3-0}{10-5}=\frac{-3}{5}$ ……..$\left(1\right)$

$\therefore$ Slope of $QR=\frac{6-(-3)}{-5-10}=\frac{9}{-15}$

$=\frac{-3}{5}$ …….$\left(2\right)$

$\therefore$ Slope of $RP=\frac{0-6}{5+5}=\frac{-6}{10}$

$=\frac{-3}{5}$ ……..$\left(3\right)$

From $\left(1\right),\left(2\right)$ & $\left(3\right)$

All points are collinear.